A spatial access-oriented implementation of a 3-D GIS topological data model for urban entities

3-D analysis in GIS is still one of the most challenging topics for research. With the goal being to model possible movement within the built environment, this paper, therefore, proposes a new approach to handling connectivity relationships among 3-D objects in urban environments in order to implement spatial access analyses in 3-D space. To achieve this goal, this paper introduces a 3-D network data model called the geometric network model (GNM), which has been developed by transforming the combinatorial data model (CDM), representing a connectivity relationship among 3-D objects using a dual graph. For the transformation, this paper presents (1) an O(n)²) algorithm for computing a straight medial axis transformation (MAT), (2) the processes for transforming phenomena from 3-D CDM to 3-D GNM, and (3) spatial access algorithms for the 3-D geometric network based upon the Dijkstra algorithm. Using the reconstructed geometric network generated from the transformations, spatial queries based upon the complex connectivity relationships between 3-D urban entities are implemented using Dijkstra algorithm. Finally, the paper presents the results of an experimental implementation of a 3-D network data model (GNM) using GIS data of an area in downtown Columbus, Ohio.